Answered

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## 9.10.3 Test (CST): Three-Dimensional Solids

Question 1 of 25

Which expression gives the volume of a sphere with radius 15?

A. [tex]\frac{4}{3} \pi\left(15^2\right)[/tex]

B. [tex]4 \pi\left(15^3\right)[/tex]

C. [tex]4 \pi\left(15^2\right)[/tex]

D. [tex]\frac{4}{3} \pi\left(15^3\right)[/tex]

Sagot :

GinnyAnswer
To determine the volume of a sphere with a given radius, we use the formula for the volume of a sphere:

[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]

In this formula, \( V \) represents the volume and \( r \) represents the radius of the sphere. We are given that the radius \( r \) is 15.

Substituting \( r = 15 \) into the formula:

[tex]\[ V = \frac{4}{3} \pi (15^3) \][/tex]

Thus, the correct expression from the given options is:

D. \(\frac{4}{3} \pi \left(15^3\right)\)

After performing the computation (raising 15 to the power of 3, multiplying by π, and then multiplying by \(\frac{4}{3}\)), the volume of the sphere is found to be approximately:

14137.166941154068 cubic units.

Therefore, the correct choice is:

D. [tex]\(\frac{4}{3} \pi \left(15^3\right)\)[/tex]
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